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{{ printedBook.courseTrack.name }} {{ printedBook.name }} An inequality with real numbers have certain properties.

A real number can never be less than or greater than itself. $x≮xandx≯x$ Therefore, a number is always equal to itself, $x=x.$

Two real numbers, $x$ and $y,$ cannot be less than and greater than each other at the same time.

If $x<y$ then $y≮x$

If $y<x$ then $x≮y$

Just like the transitive property of equality, if $x$ is less than $y$ and $y$ is less than $z,$ $x$ must be less than $z$ as well.

If $x<y$ and $y<z,$ then $x<z$

The inequality signs can be flipped and the relation will still be true.

If $x>y$ and $y>z,$ then $x>z$

The addition property applies for inequalities as well.

If $a<b,$ then $a+c<b+c$

For any given inequality it is possible to subtract a real number from both sides and the inequality will still hold true.

If $a<b,$ then $a−c<b−c$

The multiplication property for inequalities differ from the multiplication property of equality. Depending on the value of the multiplier, there are three different cases.

$x<y$ | |
---|---|

If $z>0$ | $xz<yz$ |

If $z<0$ | $xz>yz$ |

If $z=0$ | $xz=yz$ |